This brought the total amount the Bank has pumped into the economy to £200bn.
The Bank's rate-setting Monetary Policy Committee (MPC) also kept UK interest rates on hold at 0.5% for the eighth month in succession.
Mr King said the increase in inflation would be triggered by VAT returning to 17.5% on 1 January 2010 and higher petrol prices.
However, he said inflation, which is currently at 1.1%, would then fall back in the medium term.
"The past year has been extremely painful for most economies around the world," said Mr King.
"There is a more buoyant picture looking ahead, that is encouraging. But this does not alter the extent of the challenges facing the economy."
The Bank extended its quantitative easing programme last month
Former MPC member Professor David Blanchflower, who correctly predicted the recession, raised doubts about the strength of the recovery following Mr King's comments.
"A lot of what we are seeing is being driven by government stimulus. But we need to look at the real economy, and firms are not hiring. They are not laying off, but they are definitely not hiring," he said.
He also said it was only natural that the UK would take longer to recover than other countries that have already emerged from recession.
"We have a bigger financial sector, had a bigger run-up in house prices and have had less fiscal stimulus than others.
"We made more in the good times, and so lost more when the bad times hit."
The pound fell against both the euro and the dollar following the presentation of the Inflation Report, on the expectation interest rates will remain at 0.5% for some time.
Against the dollar, the pound was down 0.9% at $1.6558, while one pound was worth 1.1064 euros.
"Despite a recovery in economic growth, output is unlikely, at least for a considerable period, to return to a level consistent with a continuation of its pre-crisis period," added Mr King.
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